Math Core Curriculum/Fifth Grade/Overview Math Core Curriculum Fifth Grade Attached are 19 posters and 5 checklists for use with students. These posters have been designed to help guide Fifth Grade students in the mastery of the required math core curriculum as stated below: Operations and Algebraic Thinking 5.OA Write and interpret numerical expressions. 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Analyze patterns and relationships. 3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Number and Operations in Base Ten 5.NBT Understand the place value system. 1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 3. Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 100 + 4 10 + 7 1 + 3 (1/10) + 9 (1/100) + 2 (1/1000). Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Fifth Grade/Overview b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4. Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply multi-digit whole numbers using the standard algorithm. 6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Number and Operations Fractions 5. NF Use equivalent fractions as a strategy to add and subtract fractions. 1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Fifth Grade/Overview 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show (2/3) 4 = 8/3, and create a story context for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5. Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. 6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Fifth Grade/Overview c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Measurement and Data 5.MD Convert like measurement units within a given measurement system. 1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05m) and use these conversions in solving multi-step, real world problems. Represent and interpret data. 2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems, involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 4. Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Fifth Grade/Overview of multiplication. b. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms by adding the volumes of the non-overlapping parts applying this technique to solve real world problems. Geometry 5.G Graph points on the coordinate plane to solve real-world and mathematical problems. 1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plan located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x- axis and x-coordinate, y-axis and y-coordinate). 2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Classify two-dimensional figures into categories based on their properties. 3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles so all squares have four right angles. 4. Classify two-dimensional figures in a hierarchy based on properties. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Operations and Algebraic Thinking/Grade 5/Student Checklist Name Date MATH OPERATIONS AND ALGEBRAIC THINKING STUDENT CHECKLIST Standard 5.OA.1 I can use parentheses, brackets or braces to solve numerical expressions. I know this standard. ( ) My work that shows this: 5.OA.2 I can write simple numerical expressions. 5.OA.3 I can analyze patterns and relationships. I can graph patterns and relationships on a coordinate plane. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Number and Operations in Base Ten/Grade 5/Student Checklist Name Date MATH NUMBER AND OPERATIONS IN BASE TEN STUDENT CHECKLIST Standard 5.NBT.1 I recognize that in a large number, a digit is 10 times the value of the digit to its right. I recognize that in a large number, a digit is 1/10 the value of the digit to its left. 5.NBT.2 I can explain patterns in the number of zeros of the product when multiplying by powers of 10. I can explain patterns in the placement of the decimal point when multiplying or dividing by powers of 10. I can use exponents to show powers of 10. I know this standard. ( ) My work that shows this: 5.NBT.3 I can read and write decimals to thousandths. I can compare two decimals to thousandths. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Number and Operations in Base Ten/Grade 5/Student Checklist Name Date Standard 5.NBT.4 I can round decimals to any place. I know this standard. ( ) My work that shows this: 5.NBT.5 I can multiply multi-digit whole numbers. 5.NBT.6 I can find the quotients with up to four-digit dividends and two-digit divisors. I can explain my answer by using equations, rectangular arrays or area models. 5.NBT.7 I can add, subtract, multiply and divide decimals to hundredths. I can explain my reasoning used. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Numbers and Operations - Fractions/Grade 5/Student Checklist Name Date MATH NUMBER AND OPERATIONS - FRACTIONS STUDENT CHECKLIST Standard 5.NF.1 I can add and subtract fractions with unlike denominators. I know this standard. ( ) My work that shows this: 5.NF.2 I can solve word problems involving addition and subtraction of fractions with unlike denominators. I can mentally estimate and assess my work. 5.NF.3 I can solve word problems involving division of whole numbers leading to answers in the forms of fractions and mixed numbers. 5.NF.4 I can show how to multiply a fraction or whole number by a fraction. I can find the area of a rectangle with fractional side lengths. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Numbers and Operations - Fractions/Grade 5/Student Checklist Name Date Standard 5.NF.5 I can compare the size of a product based on the sizes of the factors. I can explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number. I can explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. 5.NF.6 I can solve real world problems involving multiplication of fractions and mixed numbers, using visual models or equations. 5.NF.7 I can explain division of a unit fraction by a non-zero whole number and find the quotient. I can explain division of a whole number by a unit fraction and find the quotient. I can solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. I know this standard. ( ) My work that shows this: Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Measurement and Data/Grade 5/Student Checklist Name Date MATH MEASUREMENT AND DATA STUDENT CHECKLIST Standard 5.MD.1 I can convert units of measure within a given measurement system. I can use these conversions to solve multi-step real world problems. 5.MD.2 I can make a line plot to display a data set of measurements in fractions. I can use a line plot and operations on fractions to solve problems. 5.MD.3 I understand and can show volume as an attribute of solid figures. 5.MD.4 I can measure volume. I know this standard. ( ) My work that shows this: 5.MD.5 I can solve real world problems involving volume, using multiplication and division. I can find the volume of a right rectangular prism with wholenumber side lengths. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
Math Core Curriculum/Geometry/Grade 5/Student Checklist Name Date MATH GEOMETRY STUDENT CHECKLIST 5.G.1 Standard I can graph points on a coordinate plane using perpendicular number lines. I know this standard. ( ) My work that shows this: 5.G.2 I can solve real world and math problems by graphing points on a coordinate plane. 5.G.3 I know and can show that attributes belonging to a group of 2-dimensional figures also belong to sub-groups of that shape. 5.G.4 I can classify 2-dimensional figures in a hierarchy based on their properties. Adapted from Common Core State Standards 2010National Governors Assoc. Center for Best Practices, Council
OPERATIONS AND ALGEBRAIC THINKING 5OA.1 2 Use parentheses, brackets or braces in NUMERICAL EXPRESSIONS Add 8 and 7, Then multiply by 2 Or 2 x (8 + 7) Math Core Curriculum/Fi h Grade/5.OA.1 2
OPERATIONS AND ALGEBRAIC THINKING 5OA.3-4 FINDING AND GRAPHING 8 7 6 5 4 3 2 1 PATTERNS 0 1 2 3 4 5 Math Core Curriculum/Fi h Grade/5.OA.3 4
NUMBER AND OPERATIONS IN BASE TEN 5.NBT.1 PLACE VALUE l l l l l l ONES TENS HUNDREDS THOUSANDS TEN THOUSANDS HUNDRED THOUSANDS MILLIONS Math Core Curriculum/Fi h Grade/5.NBT.1
NUMBER AND OPERATIONS IN BASE TEN 5.NBT.2a POWERS OF 10 10 2 = 10 X 10 = 100 10 3 = 10 X 10 X 10 = 1000 10 4 = 10 X 10 X 10 X 10 = 10,000 10 5 = 10 X 10 X 10 X 10 X 10 = 100,000 Math Core Curriculum/Fi h Grade/5.NBT.2a
NUMBER AND OPERATIONS IN BASE TEN 5.NBT.2b POWERS OF 10 Decimals 5.7804 x 10 = 57.804 5.7804 x 100 = 578.04 5.7804 x 1000 = 5780.4 3.65890 x 10 = 36.5890 3.65890 x 10 2 = 365.890 3.65890 x 10 3 = 3658.90 Math Core Curriculum/Fi h Grade/5.NBT.2b
NUMBER AND OPERATIONS IN BASE TEN 5.NBT.3-4 WRITING AND COMPARING DECIMALS Thirty four and sixteen hun- dredths 34.16 Thirty four and sixteen thousandths 34.016 Which number is the greatest? Thirty four and one tenth 34.1 Math Core Curriculum/Fi h Grade/5.NBT.3 4
NUMBER AND OPERATIONS IN BASE TEN 5.NBT.5 MULTIPLYING MULTI-DIGIT NUMBERS 825 X 46 4950 + 33000 37950 Math Core Curriculum/Fi h Grade/5.NBT.5
NUMBER AND OPERATIONS IN BASE TEN 5.NBT.6 DIVIDING LARGE NUMBERS 41 23 943-92 23-23 0 Math Core Curriculum/Fi h Grade/5.NBT.6
NUMBER AND OPERATIONS IN BASE TEN 5.NBT. 7 ADDITION DECIMALS SUBTRACTION 3.5 6.3 + 4.1-3.1 7.6 3.2 MULTIPLICATION DIVISION 1.5 3.5 X 1.1 12 42.0 1 5-36 + 150 60 1.65-60 0 Math Core Curriculum/Fi h Grade/5.NBT.7
NUMBER AND OPERATIONS FRACTIONS 5.NF.1-2a ADDING FRACTIONS With Unlike Denominators 1/2 + 1/4 Is 2/4 + 1/4 = 3/4 Math Core Curriculum/Fi h Grade/5.NF.1 2a
NUMBER AND OPERATIONS FRACTIONS 5.NF.1-2b SUBTRACTING FRACTIONS With Unlike Denominators 1/2-1/3 Is 3/6-2/6 = 1/6 Math Core Curriculum/Fi h Grade/5.NF.1 2b
NUMBER AND OPERATIONS FRACTIONS 5.NF.3 FRACTIONS AND MIXED NUMBERS 4 1/2 12 3/4 + 3 1/2-7 1/4 8 5 2/4 Math Core Curriculum/Fi h Grade/5.NF.3
NUMBER AND OPERATIONS FRACTIONS 5.NF.4-6 MULTIPLYING FRACTIONS 1/2 x 1/2 = 1/4 2 1/2 x 3 1/2 3/4 x 8 = 24/4 = 6 = 5/2 x 7/2 = 35/4 = 8 3/4 Math Core Curriculum/Fi h Grade/5.NF.4 6
NUMBER AND OPERATIONS FRACTIONS 5.NF.7 DIVISION AND FRACTIONS 3/4 IS 3 4 20/5 IS 20 5 5 1/4 = 1/2 2 = 20 1/4 Math Core Curriculum/Fi h Grade/5.NF.7
MEASUREMENT AND DATA 5.MD.1 MEASUREMENT CONVERSIONS 1000 centimeter (cm) = 1 meter (m) 1000 m = 1 kilometer (km) 1000 grams (g) = 1 kilogram (km) 1000 milliliter (ml) = 1 liter (l) 16 ounces (oz.) = 1 pound (lb.) 1 hour (hr.) = 60 minutes (min.) 1 minute = 60 seconds (sec.) Math Core Curriculum/Fi h Grade/5.MD.1
MEASUREMENT AND DATA 5.MD.2 MEASURING FRACTIONS X X X X X X X X X X X l l l l l l l l l 1/8 1/4 1/2 3/4 1 Math Core Curriculum/Fi h Grade/5.MD.2
MEASUREMENT AND DATA 5.MD.3-5 VOLUME FOR RECTANGULAR PRISMS Length x Width x Height = Volume Base x Height = Volume Math Core Curriculum/Fi h Grade/5.MD.3 5
GEOMETRY 5.G.1-2 AXIS COORDINATE PLANES 5...... 4...... 3...... 2...... 1............ 0 1 2 3 4 5 AXIS POINT Math Papers Adapted fr 201
GEOMETRY 5.G.3-4 2D FIGURES AND THEIR SUB-GROUPS Acute Triangles Scalene Equilateral Obtuse Triangles Scalene Isosceles Quadrilaterals Rhombus Square Parallelogram Math Core Curriculum/Fi h Grade/5.G.3 4